Evaluate the given integral by changing to polar coordinates.
7. where D is the top half of the disk with center the origin and radius 5
To evaluate: The given integral by changing into the polar coordinates.
The function, .
The region D is the upper semicircle centered at origin and radius 5.
If is a polar rectangle R given by where , then, (1)
If is the function of and is the function of then,
From the given region D, it is observed that the value of r varies from 0 to 5 and the value of varies from 0 to .
Substitute and in the equation (1),
Integrate the function with respect to and r by using the equation (2)
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